To determine RebRate (or Reb %), you need to know the following five things

1.The amount of rebounds the players has grabbed2.The amount of rebounds the team has grabbed3.The amount of rebounds the opposing team has grabbed4.The number of minutes the player played5.The number of minutes the entire team played

We don't have listed rebound rates for the pre-1969 era, because don't have correct totals for #2, or listed totals for #3 or, often #5. You can try and do a pace adjustment, but that's not working out Rebound Rate (more on that later). But, actually, it's not that hard to get the exact amount for #2 and #5 most of the time, and a good estimate for #3. With that in mind, here's how to estimate rebound rates for pre-1969 players.

#1. Understand the problem with using listed rebounds total for a team. Because of terminology, this will be tricky, but here goes. Prior to 1969, the NBA did not separately keep track of "team rebounds." These are rebounds that go out of bounds, and are awarded to a team. On average, these account for about 12.2% of all rebounds prior to 1969. It varies a bit, but not a whole lot...few teams are over 15 or 16%, or below 10%. For entire seasons, the variance is even less...between about 10.8% and 14.5%.

So that means we can make a guess for #3...of how many rebounds the opposing teams has grabbed. We start by multiplying the league average listed rebounds for a pre-1968 season by .878. This is the average number of rebounds a team grabbed. Substitute it in for #3, and we have half of our missing numbers.

This is also why rebound totals suddenly dropped so radically in the one year of 1969...statisticians effectively took out 12.5% of the rebounds that had been counted before. According to league stats, the average team in 1968 grabbed 5431 rebounds. In 1969, it was 4666...a drop of 14%. Was it really that huge of a drop? Nope...about 12.2% was due to the team rebounds no longer being counted.#2. How accurate is this going to be?Welllll....close enough to make a very good analysis some of the time, but not all of the time. In 1965, the average team grabbed is listed at getting 5381 rebounds. If the average without team rebounds is between 10.5% and 14.5% lower, the number will be somewhere between 4601 and 4816. Multiplying by .878 gives 4724. In other words, you're not going to be more than 100 rebounds...about 2% off from the highest and lowest variances. Usually, you'll be 1% off or under. Close. But we can make it better.

#3. How close will that be to how many actual rebounds an opposing team grabbed?Well, it will get you in the right direction. It's pretty rare to have opposing team rebound totals vary by more than 25%. Look at last year. Golden State surrendered 3860 rebounds; Portland gave up 2976. 26 out of 30 teams were between 3617 and 3187...within about 13%. Still more than a couple of teams would be pretty far out of line if we used "average" league rebounds to replace opposing team rebounds. Four teams would be off by 9.8% or more. How can we get it closer?

#4. Look at how often the team shot the ball relative to the league, and multiply that by the average.Let's try that with last year's teams as an example. Only one team out of 30 is off by more than 5.88%. Standard deviation confirms this...it's about 127 rebounds, or about 3.7%. 95% of all teams should be within 7.4% of this recalculated amount.

I've actually run it through more teams, and last year was pretty typical...the standard deviation is around 3.6%. There's no wild fluctuations in deviation as we go farther back...it will goes as high as 5% or as low as 2.5%.

What this means, though, is that 95% of the time, we'll be within about 7.2% of the league average. And since this is only ~50% of the team rebound totals we need, we could cut that deviation/error rate in half if we only knew how many rebounds a pre-1969 team had.

#5. We know how many rebounds a pre-1969 team actually had. And how many minutes the team played.Yup. It's true. And it'd kind of scandalously easy. All you do is add up all the individual player rebounds and minutes. Sometimes pre-1964 team don't have stats for all players, but most do.

So we come out with...We 've now got a system that will get us within about 3.6% over 95% of the time. If we choose a random player and compare our formula to the "true" equation, we can see how close our formula comes. Let's look at Bill Bridges of the Hawks in 1971.

The average rebounding team in 1971 grabbed 4356 rebounds. The Hawks took only 96.778 of the average amount of shots, so we multiply 4356*.96778 and get 4216 rebounds. So, we use the team total minutes/5 and the team total rebounds and Bridges' individual minutes and rebounds to use the formula for RebRate.

100 * (TRB * (Tm MP / 5)) / (MP * (Tm TRB + Opp TRB))

100*(1233*3951)/(3140*(4472+4216) = 17.86

We have estimated Bill Bridges 1971 rebound rate to be 17.86!

This, sadly, is incorrect. We know the exact amount of opponent rebounds against the Hawks in 1971...4279. So we know the actual answer is

100*(1233*3951)/(3140*(4472+4279) = 17.73

Our estimate was off by about a bit under 1%. We can look at someone where we're off by more. Let's look at someone obscure who didn't play nearly as much. Let's try David Wood on the 1995 Warriors. An average opposing team grabbed 3408 rebounds. The Warriors put up 6873 shots, about 2.86% more than the league average of 6682. 1.0286*3408 = 3505. So we plug in our other numbers and get

100*(241*3981)/(1336*(3472+3505) = 10.29

...except the Warriors were apparently a miserable team at blocking out, and didn't give up 3505 rebounds. They gave up 3723. Our estimate is off by about 6%...almost two standard deviations. this is an example that is much farther off than average; the type of estimate that will crop up maybe 10% of the time. How much does it throw off the equation?

100*(241*3981)/(1336*(3472+3723) = 9.98

Our estimate is off by about 3%. It is rare that an estimate will be off by this much. It is (much) rarer that it will be off by 4.5% or more.

What about the team rebounds estimate? Won't that potentially throw things off too?Possibly...but, again rarely, and not by much. Between 1963 and 1968, if you add up all the individual player rebounds to get actual team rebounds, and divide by the listed amount, you find that every team--100%--are between .855 and .897. The standard deviation is about .01. Twice that works out to maybe120 rebounds in the huge rebounding period of the 1960s. So, in a pretty bad case scenario, you'd be off by 120 rebounds out of 4500...less than 3%

So we add it all up...It's possible that if positively everything goes wrong, and all goes wrong in the same direction, we could be off by 2.5% by using .878 to get team rebounds, and by maybe 7% if we are on a freak team that just goes against every statistical norm. Each of these situations will happen, maybe, once out of every 30 to 50 estimated seasons...2-3% of the time. Having them both happen, and both errors going either up or down will be more rare. Let's say it happens, and both errors occur in the same direction. We should have come up with opposing 3800 team rebounds, and we got 4165 instead. For a player that played 2450 minutes out of 3960 minutes, and grabbed 345 out of his teams 3970 rebounds, here are the equations:

100*(345*3960)/(2450*(3970+3800) = 7.17

100*(345*3960)/(2450*(3970+4165) = 6.85

That's pretty much a worst case scenario. The error is under 5%. I've worked it out that 95%+ of the time, you'll be within 3.5% either way. Most of the time you should be with a couple of percent, which is really enough to use this as a tool, as far as I'm concerned.

Let's look at someone obscure who was thought to be good in his time...Neil Johnston in 1956 is a good call. He played 2594 minutes and snagged 872 rebounds. If we add up all the player rebound totals on the 1956 Warriors, we get 3897. (btw, the listed amount is 4362...the actual total is .893 of that.) If we add up all the team minutes, we get 17355. Divided by 5, that's 3471...a hair over 48.2 minutes per game in the 72 game season.

The average team in 1956 grabbed 4327 rebounds. Multiply that by .878 and get 3799. The Warriors took 6437 shots, 97.83% of the league average of 6580. .9783*3799=3717. That''s our opponent rebound estimate.

So we plug in our numbers to get

100*(872*3471)/(2594*(3897+3717) = 15.32

...which is pretty damn good. Not epic or anything, but about what you expect out of an average frontcourt starter today.

What about someone like Bob Pettit? Supposed to be a great rebounder? What about when he got old, and better players started coming in...like by 1964?

100*(1224*3865)/(3296*(4288+4539) = 16.26

...which is really good. That's more or less how Shaq and Al Horford rebounded last year. And this was a bad year for Bob.

Do I have to do all that math? And add up those numbers?Yes. Do it on a spreadsheet. You have to know how many minutes the team played. You have to know how many rebounds the team got. You already know how many rebounds the individual got and how many minutes he played. that leaves the estimate of opposing rebounds as the only variable in the equation--and if we make a decent estimate at that, our analysis will always be within an acceptable margin for error.

Is there another way to do this? One that's, you know, easier?Short answer: No.

Better answer. No. To figure out RebRate, you need to have the five numbers:

Team minutes played (to be divided by 5)Individual minutes playedIndividual reboundsTeam reboundsOpposing team rebounds

Those are the required parts of the equation. If someone claims they have something else or do something, they're not being honest. Pace adjusted estimates are not the same as RebRate. You can't use a pace adjustment to get team total rebounds or total team minutes played.

The good news is that it's pretty easy to make up a spreadsheet that will do a big party of the number crunching...all you do is enter in are the minutes and rebounds of all the players on a team.

First off..not a great rebounding team. Despite the presence of Bill Russell (who really is a legitimately great board man...Reb % of over 18.9 in this season), the Celtics were hampered by lack of a true second big man. Heinsohn was more of a scoring/no rebounding PF. Satch Sanders worked hard. But both had Reb % around 11 or 12. An “average” starting frontcourt should have a combined Reb % of around 30.5...so Russell and those guys are only a little above average.

A better rebounding team, although still not elite. Russell confirms that he rebounds as well or better as an older player by getting near 20 in Reb. %. Bailey Howell and Wayne Embry get almost all of the rest of the frontcourt minutes and are, again, lousy at around 11.5-12 in Reb %. Biggest lift for this team is at SF, where Don Nelson and Satch Sanders gave them solid play on the glass.

What about the 1968 Sixers—the year they lost in the playoffs after having dethroned the Celtics in 1967?

A much better rebounding team than either of the Celtics teams. Wilt is, as usual, over 20 in Reb %. Luke Jackson and Wilt combined for a Reb % of about 33.5, which is very good for a frontcourt combo. The SF position was strong too with Chet Walker and Billy Cunningham, and even though the team's guards did not hit the glass well, the 1968 Sixers grabbed about 51.5% of the rebounds per game...in modern pace, they'd outrebound their opponents by about 2.5 boards a game.

But Billy Cunningham...isn't he supposedly a great rebounder? Why is he (only) around 10 in Reb %? Because he played next to Wilt. Look what happened in 1969, after Wilt left.

Luke Jackson got hurt early this season (his Reb % went up as wellm though...a ten percent or so increase to around 14.6). This forced Cunningham to play PF; the Sixers were a very small team. (C—Imhoff/Green, PF—Cunningham/Jackson, SF—Walker, SG—Greer, PG—Jones.) But when we look at it by position, the Sixers lost almost all of their rebounding at a specific position...the Center position. If you compare the PFs of 1968 and 1969, you find that Cunningham rebounded about as well as Luke Jackson did in 1968. Chet Walker rebounded as well as Cunningham (and, well, Chet Walker) had in 1968. Wali Jones and Hal Greer had fairly insigificant rises in their rebounding at the guard positions. But Darrel Imhoff, Jumpin' Johnny Green and George Wilson combined for about a Reb % of about 15.5. That's a drop of about 4.7% for that position. Over 3800 minutes (which is what Imhoff/Green/Wilson played in 1969, and Wilt played in 1968), that's a difference of about 430 rebounds. The 1968 Sixers outrebounded their opponents by an estimated 300 boards; the 1969 Sixers were outrebounded by an estimated 240 boards. 80% of that difference is Wilt's leaving.

Anyway, we can see that Billy C's 13.4 Reb % in 1969 is pretty much spot on with what he did in 1971 and 1972 with the Sixers, when he continued to be a combo forward. Cunningham bulked up and actually became an even better board guy...he was a below average rebounder for a PF, but a great rebounding SF.

The last team I want to look at as an example is the 1965 Cincinnati Royals. This team is interesting because it has:

1)Oscar Robertson, who is considered to be one of the greatest (if not the greatest) rebounding PG in history.2)Jerry Lucas, who compiled a rare 20 rpg season3)Other players with good rebounding numbers in Happy Hairston and Wayne Embry.

Jerry Lucas rebounds as advertised. Any crap people want to say about “Oh, the pace/style/etc.!” is just that...crap. Dude has a Reb % of about 19. That's fantastic.

Oscar, on the other hand, has some of his mystique taken. His rebound % is a bit over 8.1%. That's very good for a PG. But, well, it's a long way from being super elite. Chris Paul rebounds at that level or better. Andre Miller is close; so is Gary Payton. Rondo is better. Kidd is much better. Put it this way; at 40 mpg in the 2009, the Big O would have averaged about 5.5 boards a game.

Wayne Embry, as with the Celtics, is not a particularly good rebounder. I think this comes form two factors. One was his pick setting ability and the fact that this skill pulled him out of the key a lot. The other was that Lucas, like Russell, took some rebounds from him.

And, when you get down to it, the 1965 Royals were not a great rebounding team. On the surface, you would wonder why..you've got Lucas, Oscar, Embry, etc. But, as with some other teams, deficiencies in rebounding at other positions hurt them. Jack Twyman was a below average rebounder at SF (7.0 Reb %). Adrian Smith was a terrible rebounder for a SG (3.3 Reb %). When you add up Oscar, Smith, and Twyman, you get a combined Reb % of about 18.5%. That's average, or even a little below. Embry, as I noted, was below average. But Lucas made up those deficiencies and then some, allowing the team to be a pretty good (not great) rebounding team.

Biff wrote:Hopefully this will help people realize how vastly inflated numbers were back in those days. Rodman was every bit as good of a rebounder as Chamberlain and Russell, with a career TRB% of 23.

There is the problem of discussing a specialist rebounder like Rodman in context with a guy who was doing that sort of thing for a lot more games per season while also being an offensive hub. That cannot be ignored either, no matter how awesome Rodman truly was.

Biff wrote:Hopefully this will help people realize how vastly inflated numbers were back in those days. Rodman was every bit as good of a rebounder as Chamberlain and Russell, with a career TRB% of 23.

There is the problem of discussing a specialist rebounder like Rodman in context with a guy who was doing that sort of thing for a lot more games per season while also being an offensive hub. That cannot be ignored either, no matter how awesome Rodman truly was.

Well said. Rodman is a true outlier as well as being a total role player.

In terms of inflation of statistics...I think that's very overstated. I think anyone who knows much about basketball realizes that comparisons between different eras means you can't make apples to apples comparisons in terms of raw stats. This is not much a surprise...so I think people already "realize how vastly inflated numbers were back in those days."

What I think is a lot more interesting is how you can draw distinct comparisons between past players and current players. I've said this before, but Elgin Baylor, as a rebounder is a lot like Shawn Marion or Larry Bird. Guys like Jerry Lucas come across very well. And there are some people that are just off the charts. I've heard a lot more about the tragedy of Maurice Stokes than Mo Stokes the basketball player. But when I did his rebound numbers, they were astonishing. He rebounded like Dwight Howard, Wilt, or Russell. I'm actually more impressed by Reb % of older players like Bill Bridges nad Paul Silas than I am by their raw number totals.

A few years back (more than a few perhaps), I developed a formula for estimating opponent rebounds.First, multiply these known totals by their coefficients:Min * .009FGX * .3179FTX * .091Reb * .1744Ast * -.168PF * .1348Pts * .1136OppPts * .0998(FGX and FTX are missed shots)

Sum all these and multiply by 2 additional Team factors:(W/L)^.0083(Pts/OppPts)^(-.371)

These factors seemed to give best fit between estimated and actual OppReb for all NBA teams, 1971-1974.The average (absolute) error was 145. That's 1.77 Reb/G.

jicama wrote:Hi, first post. Using a fake name, as is apparently the custom here.

A few years back (more than a few perhaps), I developed a formula for estimating opponent rebounds.First, multiply these known totals by their coefficients:Min * .009FGX * .3179FTX * .091Reb * .1744Ast * -.168PF * .1348Pts * .1136OppPts * .0998(FGX and FTX are missed shots)

Sum all these and multiply by 2 additional Team factors:(W/L)^.0083(Pts/OppPts)^(-.371)

These factors seemed to give best fit between estimated and actual OppReb for all NBA teams, 1971-1974.The average (absolute) error was 145. That's 1.77 Reb/G.

I'm not sure I understand.

Would you care to elaborate on what each of the factors are ?

For Example, is Min - the total minutes played by the year in a given season ? But Reb is the total rebs by the team in a given season ?

The way you describe Cunningham reminds of none other than Josh Smith a great rebounding SF but a mediocre rebounding PF who fans overrate and "romanticize" his athletic ability being able to overcome his lack of height.

I aint got no time, I gotta get mine. I keep my mind on my loot I'll shoot every time.

Would anyone mind using the method of the OP to fill in the rebound rate for Wilt? See link below. Drtg and Ortg would be great too, if anyone is able. I just don't have the time to do it myself and was wondering if anyone else had done it or is thinking about doing it. Thank you sincerely for posting if you do.

2) What about calculations for the playoffs? I'm considering calculating a weighted average (for the teams faced in the postseason) of opposition TRB in my spreadsheets to replace league average, which seems fine.

Providing proper context is not making excuses. Correcting false narratives is not revising history.

I put together spreadsheets with the calculations for each team in the regular season and playoffs from 54-55 through 69-70. As a bonus, I filled out the assist numbers from 54-55 through 63-64 (regular season only, B-R already has playoff numbers) since those were also missing. Here are the links:

For a few of the earlier regular seasons, certain players have missing lines (I presume this is due entirely to trades). For those team seasons, I've used the team rebounds (times 0.878 through 67-68), team FGA, from the B-R totals. For team minutes, I just calculated 5*(nGames*48+nOT*5), going through the gamelogs.

In case anybody is interested, here are the top 10s for missing years: